Parameter Estimation in the Age of Degeneracy and Unidentifiability

Parameter estimation from observable or experimental data is a crucial stage in any modeling study. Identifiability refers to one’s ability to uniquely estimate the model parameters from the available data. Structural unidentifiability in dynamic models, the opposite of identifiability, is associated with the notion of degeneracy where multiple parameter sets produce the same pattern. Therefore, the inverse function of determining the model parameters from the data is not well defined. Degeneracy is not only a mathematical property of models, but it has also been reported in biological experiments. Classical studies on structural unidentifiability focused on the notion that one can at most identify combinations of unidentifiable model parameters. We have identified a different type of structural degeneracy/unidentifiability present in a family of models, which we refer to as the Lambda-Omega (Λ-Ω) models. These are an extension of the classical lambda-omega (λ-ω) models that have been used to model biological systems, and display a richer dynamic behavior and waveforms that range from sinusoidal to square wave to spike like. We show that the Λ-Ω models feature infinitely many parameter sets that produce identical stable oscillations, except possible for a phase shift (reflecting the initial phase). These degenerate parameters are not identifiable combinations of unidentifiable parameters as is the case in structural degeneracy. In fact, reducing the number of model parameters in the Λ-Ω models is minimal in the sense that each one controls a different aspect of the model dynamics and the dynamic complexity of the system would be reduced by reducing the number of parameters. We argue that the family of Λ-Ω models serves as a framework for the systematic investigation of degeneracy and identifiability in dynamic models and for the investigation of the interplay between structural and other forms of unidentifiability resulting on the lack of information from the experimental/observational data.

Enabling Systems Innovation in Climate Change Adaptation: Exploring the Role for MEL

Traditional monitoring, evaluation, and learning (MEL) approaches, methods, and tools no longer reflect the dynamic complexity of the severe (or “super-wicked”) problems that define the Anthropocene: climate change, environmental degradation, and global pandemics. In late 2019, the Adaptation Fund’s Technical Evaluation Reference Group (AF-TERG) commissioned a study to identify and assess innovative MEL approaches, methods, and technologies to better support and enable climate change adaptation (CCA) and to inform the Fund’s own approach to MEL. This chapter presents key findings from the study, with seven recommendations to support a systems innovation approach to CCA: Promote and lead with a CCA systems innovation approach, engaging with key concepts of complex systems, super-wicked problems, the Anthropocene, and socioecological systems. Engage better with participation, inclusivity, and voice in MEL. Overcome risk aversion in CCA and CCA MEL through field testing new, innovative, and often more risky MEL approaches. Demonstrate and promote using MEL to support and integrate adaptive management. Work across socioecological systems and scales. Advance MEL approaches to better support systematic evidence and learning for scaling and replicability. Adapt or develop MEL approaches, methods, and tools tailored to CCA systems innovation.

Forward Bifurcation with Hysteresis Phenomena from Atherosclerosis Mathematical Model

Atherosclerosis is a non-communicable disease (NCDs) which appears when the blood vessels in the human body become thick and stiff. The symptoms range from chest pain, sudden numbness in the arms or legs, temporary loss of vision in one eye, or even kidney failure, which may lead to death. Treatment in cases with severe symptoms requires surgery, in which the number of doctors or hospitals is limited in some countries, especially countries with low health levels. This article aims to propose a mathematical model to understand the impact of limited hospital resources on the success of the control program of atherosclerosis spreads. The model was constructed based on a deterministic model, where the hospitalization rate is defined as a time-dependent saturated function concerning the number of infected individuals. The existence and stability of all possible equilibrium points were shown analytically and numerically, along with the basic reproduction number. Our analysis indicates that our model may exhibit various types of bifurcation phenomena, such as forward bifurcation, backward bifurcation, or a forward bifurcation with hysteresis depending on the value of hospitalization saturation parameter and the infection rate for treated infected individuals. These phenomenon triggers a complex and tricky control program of atherosclerosis. A forward bifurcation with hysteresis auses a possible condition of having more than one stable endemic equilibrium when the basic reproduction number is larger than one, but close to one. The more significant value of hospitalization saturation rate or the infection rate for treated infected individuals increases the possibility of the stable endemic equilibrium point even though the disease-free equilibrium is stable. Furthermore, the Pontryagin Maximum Principle was used to characterize the optimal control problem for our model. Based on the results of our analysis, we conclude that atherosclerosis control interventions should prioritize prevention efforts over endemic reduction scenarios to avoid high intervention costs. In addition, the government also needs to pay great attention to the availability of hospital services for this disease to avoid the dynamic complexity of the spread of atherosclerosis in the field.

Complexity of COVID-19 Dynamics

With population explosion and globalization, the spread of infectious diseases has been a major concern. In 2019, a newly identified type of Coronavirus caused an outbreak of respiratory illness, popularly known as COVID-19, and became a pandemic. Although enormous efforts have been made to understand the spread of COVID-19, our knowledge of the COVID-19 dynamics still remains limited. The present study employs the concepts of chaos theory to examine the temporal dynamic complexity of COVID-19 around the world. The false nearest neighbor (FNN) method is applied to determine the dimensionality and, hence, the complexity of the COVID-19 dynamics. The methodology involves: (1) reconstruction of a single-variable COVID-19 time series in a multi-dimensional phase space to represent the underlying dynamics; and (2) identification of “false” neighbors in the reconstructed phase space and estimation of the dimension of the COVID-19 series. For implementation, COVID-19 data from 40 countries/regions around the world are studied. Two types of COVID-19 data are analyzed: (1) daily COVID-19 cases; and (2) daily COVID-19 deaths. The results for the 40 countries/regions indicate that: (1) the dynamics of COVID-19 cases exhibit low- to medium-level complexity, with dimensionality in the range 3 to 7; and (2) the dynamics of COVID-19 deaths exhibit complexity anywhere from low to high, with dimensionality ranging from 3 to 13. The results also suggest that the complexity of the dynamics of COVID-19 deaths is greater than or at least equal to that of the dynamics of COVID-19 cases for most (three-fourths) of the countries/regions. These results have important implications for modeling and predicting the spread of COVID-19 (and other infectious diseases), especially in the identification of the appropriate complexity of models.

Parameter estimation in the age of degeneracy and unidentifiability

Parameter estimation from observable or experimental data is a crucial stage in any modeling study. Identifiability refers to one's ability to uniquely estimate the model parameters from the available data. Structural unidentifiability in dynamic models, the opposite of identifiability, is associated with the notion of degeneracy where multiple parameter sets produce the same pattern. Therefore, the inverse function of determining the model parameters from the data is not well defined. Degeneracy is not only a mathematical property of models, but it has also been reported in biological experiments. Classical studies on structural unidentifiability focused on the notion that one can at most identify combinations of unidentifiable model parameters. We have identified a different type of structural degeneracy/unidentifiability present in a family of models, which we refer to as the Lambda-Omega (\Ldaomega) models. These are an extension of the classical lambda-omega (\ldaomega) models that have been used to model biological systems, and display a richer dynamic behavior and waveforms that range from sinusoidal to square-wave to spike-like. We show that the \Ldaomega\, models feature infinitely many parameter sets that produce identical stable oscillations, except possible for a phase-shift (reflecting the initial phase). These degenerate parameters are not identifiable combinations of unidentifiable parameters as is the case in structural degeneracy. In fact, reducing the number of model parameters in the \Ldaomega\, models is minimal in the sense that each one controls a different aspect of the model dynamics and the dynamic complexity of the system would be reduced by reducing the number of parameters. We argue that the family of \Ldaomega\, models serves as a framework for the systematic investigation of degeneracy and identifiability in dynamic models and for the investigation of the interplay between structural and other forms of unidentifiability resulting on the lack of information from the experimental/observational data.

Economic Evaluation of Community-Based Falls Prevention Interventions: A Systematic Methodological Overview of Systematic Reviews

Background: Falls impose significant health and economic burdens on older people, making their prevention a priority for care decision-makers. The volume of falls prevention economic evaluations has increased, the findings from which have been synthesised by systematic reviews (SRs) with pre-specified criteria (e.g., objectives, eligibility, data extraction). Such SRs can inform commissioning and design of future evaluations, particularly decision models; however, their findings can be biased and partial dependent on their pre-specified criteria. This study aims to conduct a systematic overview (SO) to: (1) systematically identify SRs of community-based falls prevention economic evaluations; (2) describe the methodology and findings of SRs; (3) critically appraise the methodology of SRs; and (4) suggest commissioning recommendations based on SO findings. Methods: The SO followed the PRISMA guideline and the Cochrane guideline on SO, covering the period 2003-2020. Identified SRs’ aims, search strategies and results, extracted data fields, quality assessment methods and results, and commissioning and research recommendations were synthesised. The comprehensiveness of previous SRs’ data synthesis was judged against criteria drawn from expert guideline and academic literature on falls prevention/public health economic evaluation. Outcomes of general population, lifetime decision models were re-analysed to inform commissioning recommendations. The SO protocol is registered in the Prospective Register of Systematic Reviews (CRD42021234379).Results: Seven SRs were identified, which extracted 8 to 33 data fields from 44 relevant economic evaluations. Four economic evaluation methodological/reporting quality checklists were used; three SRs narratively synthesised methodological features to varying extent and focus. SRs generally did not appraise decision modelling features, including methods for characterising dynamic complexity of falls risk and intervention need. Their commissioning recommendations were based mainly on cost-per-unit ratios (e.g., incremental cost-effectiveness ratios) and neglected aggregate impact. There is model-based evidence of multifactorial and environmental interventions, home assessment and modification and Tai Chi being cost-effective but also the risk that they exacerbate social inequities of health. Conclusions: Current SRs of falls prevention economic evaluations do not holistically inform commissioning and evaluation design. Accounting for broader decisional factors including intervention reach and capacity constraints and a broader grasp of methodological nuances of economic evaluations, particularly decision models, are needed.

Dynamic Complexity of Parity Exists Queries

Given a graph whose nodes may be coloured red, the parity of the number of red nodes can easily be maintained with first-order update rules in the dynamic complexity framework DynFO of Patnaik and Immerman. Can this be generalised to other or even all queries that are definable in first-order logic extended by parity quantifiers? We consider the query that asks whether the number of nodes that have an edge to a red node is odd. Already this simple query of quantifier structure parity-exists is a major roadblock for dynamically capturing extensions of first-order logic. We show that this query cannot be maintained with quantifier-free first-order update rules, and that variants induce a hierarchy for such update rules with respect to the arity of the maintained auxiliary relations. Towards maintaining the query with full first-order update rules, it is shown that degree-restricted variants can be maintained.

A Model-Based Strategy for Developing Sustainable Cosmetics Small and Medium Industries with System Dynamics

Global customer consciousness for more sustainable products and government requirements for a more sustainable industry have motivated cosmetics small and medium industries (SMIs) to innovate the strategy by integrating sustainability principles into their manufacturing processes. However, the dynamic complexity of balancing sustainability efforts, stakeholders’ interests, and uncertainty in material pricing require a conceptual reference model to help managers and decision-makers cope with the transition process. This work therefore proposes a model-based strategy using system dynamics to assist managers and stakeholders in SMIs to clarify their possible pathways and to offer a framework to understand, guide, and generate future strategies. In multiactor, multistakeholder conditions, the proposed methodology can provide insights into how stakeholders can effectively intervene to improve sustainability through open innovation dynamics models. The case study presented here on a personal care cosmetics company demonstrates several leverage points and obstacles, thereby allowing each stakeholder to understand their strategic role in realizing sustainable cosmetics SMIs.

Developmental dynamics of the neural crest-mesenchymal axis in creating the thymic microenvironment

The thymic stroma is composed of epithelial and non-epithelial cells that collectively provide separate microenvironments controlling the homing of blood-born precursors to the tissue, and their subsequent differentiation to functionally mature and correctly selected T cells. While thymic epithelial cells are well characterized for their role in thymopoiesis, a comparably comprehensive analysis of the non-epithelial thymic stroma is lacking. Here we explore at single cell resolution the complex composition and dynamic changes that occur over time in the non-epithelial stromal compartment. We detail across different developmental stages in human and mouse thymus, and in an experimental model of Di George syndrome, the most common form of human thymic hypoplasia, the separate transcriptomes of mouse mesothelium, fibroblasts, neural crest cells, endothelial and vascular mural cells. The detected gene expression signatures identify novel stromal subtypes and relate their individual molecular profiles to separate differentiation trajectories and functions. Specifically, we demonstrate an abundance and unprecedented heterogeneity of diverse fibroblast subtypes that emerge at discrete developmental stages and vary in their expression of key regulatory signalling circuits and components of the extracellular matrix. Taken together, these findings highlight the dynamic complexity of the non-epithelial thymus stroma and link the cells' specific gene expression profiles to separate instructive roles essential for normal thymus organogenesis and tissue maintenance.